Efficient evaluation of reverberant sound fields

An image method due to Allen and Berkley (1979) is often used to simulate the effect of reverberation in rooms. This method is relatively expensive computationally. We present a fast method for conducting such simulations using multipole expansions. For M real and image sources and N evaluation points, while the image method requires O(MN) operations, our method achieves the calculations in O(M + N) operations, resulting in a substantial speedup. Applications of our technique are also expected in simulation of virtual audio.